Never happened to me. Here's a pic that is not exactly like what you describe but I could see how a ball can get embedded on the lip of a bunker and be lost. Didn't something happen to Rory in the US Open?

Yup, playing in Hilton Head last year. Par 3, hit it thin, and it disappears on me. Brother found a "lump" in the sand, tucked under the sod lip.
brush away a tickle of sand, and there's my ball marking, so I was able to ID it.
Buddies were all laughing, thinking I was sure to lose the hole (whoever loses the hole when the drink cart comes y has to buy).

Well, close the face almost where the toe is pointing at the ball, take a heck of a swing, and she pops out, and rolls to about 10' haha
Buddy was rattled, and drinks were on him :-D

I lost one last year on Bandon Trails hole #5. Hit a low screamer into the front bunker under the lip but we never found it. Only one I lost on that trip.

Not exactly like that but close. 21* hybrid from about 180 out saw it splash in the bunker just left of the green. Walked up expecting to see it had rolled to the bottom. Not that lucky. After a casual look and wondering ok where did it go, took a close look at the splash mark and saw a little white dot. Yay, lucky me. Hit behind the ball (I think) as hard as I could. Almost cleared the lip but rolled back to the bottom. Got it out and 2 putted from there.

So how did you handle it?

In response to what to do, this is where it gets interesting.In my case, the ball got stuck under the sod lip.All agreed it was the only place it could be.I knelt down on the edge, searching with my hands, to no avail. What I diid find was an animal hole, because my arm went in up to the elbow.In most situations like that I would have been awarded relief, but because I couldn't pinpoint exactly (only approximately)where it went in,I had to play it as a lost ball in a hazard, which is what a bunker is. I took a drop, nearest point no nearer the hole, to where the ball entered the bunker,1 stroke penalty.I hit my 4th shot on the green and 2 putted for a double.

Of note: I play a muni and we have no pro, so that particular ruling may or may not have been correct.

Yes, have seen it happen 3 or 4 times that I can think of. Faces of the bunkers here in south Florida are pretty soft, especially in the summer when afternoon downpours wash out the bunkers, and sand has to be raked up the faces each morning. Unless you know precisely where to look it can be very difficult to spot the plugged ball.

Even more unusual situation happened a couple years ago, when someone I was playing with hit their ball, which hit a tree and came back and went under his golf cart and lodged somewhere underneath inside the cart and we could not find the ball. In that situation, he was granted free relief.